646,140

2² × 3 × 5 × 11² × 89

646,140 factors as 2^2 × 3 × 5 × 11^2 × 89. Its 72 positive divisors give a proper-divisor sum of 1,364,820, so this integer is abundant. The Collatz stopping time is 278 steps.

Prime Factor Structure

Factorization String 2^2 × 3 × 5 × 11^2 × 89

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 72

Divisor Sum (σ) 2,010,960

Proper Divisor Sum 1,364,820

Digit Sum / Digital Root 21 (Root: 3)

Adjacent Primes #646103 ← → #646147

Radix Representation

Decimal	646140
Binary	10011101101111111100 (20 bits)
Octal	0o2355774
Hexadecimal	0x9DBFC

Divisor Catalog (60 of 72)

1 2 3 4 5 6 10 11 12 15 20 22 30 33 44 55 60 66 89 110 121 132 165 178 220 242 267 330 356 363 445 484 534 605 660 726 890 979 1,068 1,210 1,335 1,452 1,780 1,815 1,958 2,420 2,670 2,937 3,630 3,916 4,895 5,340 5,874 7,260 9,790 10,769 11,748 14,685 19,580 21,538

Collatz Trajectory (278 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

646,140 323,070 161,535 484,606 242,303 726,910 363,455 1,090,366 545,183 1,635,550 817,775 2,453,326 1,226,663 3,679,990 1,839,995 5,519,986 2,759,993 8,279,980 4,139,990 2,069,995 6,209,986 3,104,993 9,314,980 4,657,490 2,328,745 6,986,236 3,493,118 1,746,559 5,239,678 2,619,839 7,859,518 3,929,759 11,789,278 5,894,639 17,683,918 8,841,959 26,525,878 13,262,939 39,788,818 19,894,409 59,683,228 29,841,614 14,920,807 44,762,422 22,381,211 67,143,634 33,571,817 100,715,452 50,357,726 25,178,863 75,536,590 37,768,295 113,304,886 56,652,443 169,957,330 84,978,665 254,935,996 127,467,998 63,733,999 191,201,998

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